Consider the infinite-space version of the billiard or carrom board problem: hard discs are initially at rest and uniformly distributed in the half-space \(x\ge 0\) , and the system is perturbed by kicking a particle near the origin in the \(x\)  direction. The moving particle eventually hits a particle at rest creating further collisions and generating a cascade penetrating the occupied half-space. Particles are also ejected back and a splash-like pattern is formed [see Fig. (REF )]. This splash problem can be thought of as a billiard with no walls and an infinite number of particles. Despite a simple formulation, the splash problem greatly differs from traditionally studied billiards systems [1]}, [2]}. The splash problem was mentioned in [3]}, [4]}. Here we provide the first detailed treatment for the one-dimensional version of the problem.
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